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m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n

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New post 03 Jul 2020, 01:52
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[GMAT math practice question]

\(m\) is an even integer, and \(n\) is an odd integer. What is \((-1)^{mn} (-1)^{m-n} {(-1)^{2m-1}(3 + 2) - (-1)^{2n}(3 - 2)}\)?

A. \(2\)

B. \(4\)

C. \(6\)

D. \(8\)

E. \(10\)

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Re: m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n  [#permalink]

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New post 03 Jul 2020, 02:01
1
Odd*even = even
Even - odd = odd
2(even)-1 = odd
2(odd) = even

-1^even = 1
-1^odd = -1

1*(-1)*(-1)*(3+2)-(1)(3-2)
5-1 => 4

MathRevolution I think answer should be four. Because (-1)^odd in order for the answer to be six. Kindly check.

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Re: m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n  [#permalink]

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New post 03 Jul 2020, 02:08
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Re: m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n  [#permalink]

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New post 03 Jul 2020, 02:12
MathRevolution wrote:
[GMAT math practice question]

\(m\) is an even integer, and \(n\) is an odd integer. What is \((-1)^{mn} (-1)^{m-n} {(-1)^{2m-1}(3 + 2) - (-1)^{2n}(3 - 2)}\)?

A. \(2\)

B. \(4\)

C. \(6\)

D. \(8\)

E. \(10\)


\((-1)^{mn} (-1)^{m-n} {(-1)^{2m-1}(3 + 2) - (-1)^{2n}(3 - 2)} =
(-1)^{even} (-1)^{odd} {(-1)^{odd}(3 + 2) - (-1)^{even}(3 - 2)} = (1)(-1)(-1)(5) - (1)(1) = 5 -1 = 4\)
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Re: m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n  [#permalink]

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New post 03 Jul 2020, 02:23
the correct answer is Option B.

MathRevolution : please check once.
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Re: m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n  [#permalink]

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New post 03 Jul 2020, 02:25
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Re: m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n  [#permalink]

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New post 03 Jul 2020, 03:01
Eplanation:

(-1)^even * (-1)^odd * (-1)^odd * (3+2) - (-1^even)*(3-2)
= 5-1
=4

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m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n  [#permalink]

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New post 05 Jul 2020, 18:20
=>

\((-1)^{mn} (-1)^{m-n}(-1)^{2m-1}(3+2) - (-1)^{2n}(3-2)\)

\(= (-1)^{even·odd} (-1)^{even-odd}(-1)^{2·even-1}(5) - (-1)^{2·odd}(1)\)

\(= (-1)^{even} (-1)^{odd} (-1)^{odd}(5) - (-1)^{even}(1)\)

\(= 1·(-1)·(-1)·5 - 1·1\)

\(= 5 - 1\)

\(= 4.\)

Therefore, B is the correct answer.
Answer: B
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m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n   [#permalink] 05 Jul 2020, 18:20

m is an even integer, and n is an odd integer. What is (-1)mn (-1)m-n

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